# meshing of parametric 3d models

I would like to do CFD analysis on a parametric model and would like to obtain mesh deformation in the parametric space.

As a concrete 2D example let us consider a house shape with a bottom rectangle and a triangle sitting on top. This shape has 3 parameters: (A) the width of the rectangle, (B) the height of the rectangle and (C) the height of the triangle. Let us choose A=10, B=8 and C=4, and then I can calculate the coordinates of this 5-point polygon from this. Moreover, I can also calculate the partial derivatives of these coordinates with respect to A, B and C.

So we have a boundary polygon where the partial derivatives of the coordinates with respect to a list of parameters are known. I would like to mesh this polygon in a way that (1) it is "nice" for CFD analysis, which many tools can achieve, (2) I would like to know the partial derivatives of the added mesh points with respect to my original parameter space.

I have not found any way to do (2). Basically I have arbitrary number of parameters assigned to initial points and would like to do meshing so that these parameters are linearly propagated (when adding a midpoint of a line segment then the parameters should be averaged). Is there any way to do this?